Research on neonatal cognition has developed very recently in comparison with the long history of research on child behavior. The last sixty years of research have provided a great amount of evidence for infants’ numerous cognitive abilities. However, only little of this research concerns newborn infants. What do we know about neonatal cognition? Using a variety of paradigms, researchers became able to probe for what newborns know. Amongst these results, we can distinguish several levels of cognitive abilities. First, at the perceptual or sensory level, newborns are able to process information coming from the social world and the physical objects through all their senses. They are able to discriminate between object shapes and between faces; that is, they are able to detect invariants, remember and recognize them. Second, newborns are able to abstract information, to compare different inputs and to match them across different sensory modalities. We will argue that these two levels can be considered high-level cognitive abilities: they constitute the foundations of human cognition. Furthermore, while some perceptual competencies can stem from the fetal period, many of these perceptual and cognitive abilities cannot be a consequence of the environment surrounding the newborn before birth.